Direct and inverse scalar scattering problems for the Helmholtz equation in R m

The boundary value problem for the Helmholtz equation in the m-dimensional free space is considered. The problem is reduced to the Lippmann-Schwinger integral equation over the inhomogeneity domain. The operator of the integral equation is shown to be an invertible Fredholm operator. The inverse coefficient problem is considered. An application of the two-step method reduces the inverse problem to the source-type integral equation with a smooth kernel. Special classes of solutions to this equation are introduced. The uniqueness of a solution to the integral equation of the first kind is proved in the defined function classes.